Download Lines, Lines, Lines!!! Standard Form of a Linear Equation ~ Lesson

Lines, Lines, Lines!!! Standard Form of a Linear Equation
Lines, Lines, Lines!!!
Standard Form of a Linear Equation
~
Lesson Plan
I.
Topic:
II.
Goals and Objectives:
A. The students will convert equations into standard form.
B. The students will write equations in standard form.
C. The students will find the coefficients of the equations.
III.
Massachusetts Learning Standards:
IV.
Standard Form
1.
8.P.6
Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a
function of x with parameters m and b.
2.
8.P.7
Set up and solve linear equations and inequalities with one or two variables, using
algebraic methods, models, and/or graph.
3.
10.P.2
Demonstrate an understanding of the relationship between various representations of a
line. Determine a line’s slope and x- and y-intercepts from its graph or from a linear
equation that represents the line. Find a linear equation describing a line from a graph or
geometric description of the line, e.g, by using the “point-slope” or “slope y-intercept”
formulas. Explain the significance of a positive, negative, zero, or undefined slope.
4.
10.P.8
Solve everyday problems that can be modeled using systems of linear equations or
inequalities. Apply algebraic and graphical methods to the solution. Use technology when
appropriate. Include mixture, rate, and work problems.
Materials:
A. Whiteboard with dry-erase markers (Blackboard with chalk could also be used.).
B. Ruler.
C. Pencils.
D. Calculator.
E. Graphing paper.
F. Standard Form Worksheets (Practice Worksheet, Quiz Worksheet).
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
V.
Presentation Outline:
A.
Introductions. "The Standard Form of a line."
I. Equation
II. Definition
B.
Write an equation in Standard Form from the given linear equation.
Example
C.
Write an equation in Standard Form given a point and a Slope
Example
D.
Write an equation in Standard Form given two points.
Example
VI.
Presentation:
A. Presentation Notes
B. Power Point Presentation
VII.
Independent Practice:
Standard Form Worksheet
A. Class work:
# 1 - 29 Odds
B. Homework:
#s 2 - 30 Evens
C. Due 2 days from given day. Allow students to complete those questions which they did not
complete in class.
VIII.
Topic Assessment: Standard Form Quiz
A. Answer questions from homework.
B. 5 Question Quiz:
10 – 15 minutes
C. 10 Question Quiz: 15 – 20 minutes
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Lines, Lines, Lines!!!
~
Standard Form of a Linear Equation
Introduction
All of the linear equations we have studied so far can be written in Standard Form.
The Standard form of a linear equation helps us identify its coefficients along with
an easiness of graphing a line by finding the x- and y- intercept of such a line. The
Standard Form is acquired when all of the criteria are met.
Definitions and Formula
The Standard Form of a linear equation is
following criteria must be met:
. However, each of the
A, B, and C are integers.
Remember:
Integers are positive and negative numbers including zero which do not have
fractions or decimals. i.e. (...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...).
A, B, and C's greatest common factor is 1.
Remember:
When two numbers have a greater common factor of 1, then they cannot be divided
by any other number than one. i.e. (3 and 5), (10 and 7), (3, 9, and 8), (-4, 11).
'A' is greater than or equal to Zero
.
A and B are not both Zero.
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Key Concepts
It is important to learn how to recognize when an equation is in the Standard form
and when it is not.
The following lines are in Standard Form
A.

Where A = 5, B = -7, and C = 6
B.

Where A = 1, B = 3, and C = 0
C.

Where A = 1000, B = 10,000, and C = 1
D.

Where A = 0, B = 1, and C = 4
The following lines are not in Standard Form:
A.

'A' and 'B' must be on the same side.
B.

'A' must be greater than or equal to Zero.
C.

These numbers can be divided by 7.
D.

E.
0x + 0y = 4

is not an integer.
'A' and 'B' can't both be Zero.
The following lines are in the form of other equations which we will learn or have learned:
A.
y = mx + b
B.

Slope-Intercept Form

Point-Slope Form
C.
Ax + By = C

Standard Form
D.
y=b

Horizontal Line (Zero Slope)
E.
x=b

Vertical Line (Undefined Slope)
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Let's see a few ways to use or find the Standard Form of a linear equation.
1. Write an equation in Standard Form from the given linear equation.
A.
i. Original equation.
ii. Add -4x to both sides.
iii. Simplify.
A = 4, B = 1, and C = 8
B.
i. Original equation.
ii. Subtract 8 from both sides.
iii. Simplify.
iv. Add -9y to both sides.
v. Simplify.
A = 3, B = 9, and C = -8
C.
i. Original equation
ii. Multiply all terms by 5.
iii. Simplify.
iv. Subtract 3x from both sides.
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
v. Simplify.
vi. Multiply all terms by -1.
vii. Simplify.
A = 3, B = -5, and C = -25
D.
i. Original equation.
ii. Multiply all terms by 12.
iii. Simplify.
A = 8, B = -3, and C = 72
2. Write an equation in Standard Form given a point and a slope.
Note:
It is always best to used the Point-Slope Form of an equation when the only
information given is one point and the slope of the linear equation.
A.
m = and point (3, 4)
i. Point-Slope Form.
ii. Substitute the information given.
iii. Simplify using the Distributive Property.
iv. Multiply all terms by 2.
v. Simplify.
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
vi. Subtract both by sides by x.
vii. Simplify.
viii. Add 8 to both sides.
ix. Simplify.
x. Multiply all terms by -1.
xi. Simplify.
A = 1, B = -2, and C = -5
B.
m = 1 and point (-2, 1)
i. Point-Slope Form
ii. Substitute the information given.
iii. Simplify using the Distributive Property.
iv. Subtract both by sides by x.
v. Simplify.
vi. Add 1 to both sides.
vii. Simplify.
viii. Multiply all terms by -1.
ix. Simplify.
A = 1, B = -1, and C = -3
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
C.
m = -3 and point (0, -8)
i. Point-Slope Form
ii. Substitute the information given.
iii. Simplify using the Distributive Property.
iv. Simplify.
v. Subtract both by sides by 8.
vi. Simplify.
vii. Add 3x to both sides.
viii. Simplify.
A = 3, B = 1, and C = -8
3. Write an equation in Standard Form given two points.
Note:
(The following examples were used on the previous lesson on Slope-Intercept Form)
A. Write an equation of the line in Standard Form which passes through
(-1, 4) and (1, -2).
i. Find the slope between the two points.
ii. Find the value of the y-intercept (b) by substituting
the value of one of the points into the equation.
iii. Simplify and solve.
iv. Substitute the value of ‘b’ into the equation.
v. Add -3x to both sides.
vi. Simplify.
A = 3, B = 1 and C = 1
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
B. Write an equation of the line in Standard Form which passes through
(5, -3) and (-4, 3).
i. Find the slope between the two points.
ii. Find the value of the y-intercept (b) by substituting
the value of one of the points into the equation.
iii. Simplify and solve.
iv. Substitute the value of ‘b’ into the equation.
v. Add
to both sides.
vi. Simplify.
vii. Multiply all terms by 3.
viii. Simplify.
A = 3, B = 3 and C = 1
C. Write an equation of the line in Standard Form which passes through
(-1, 2) and (3, 4).
i. Find the slope between the two points.
ii. Find the value of the y-intercept (b) by substituting
the value of one of the points into the equation.
iii. Simplify and solve.
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
iv. Substitute the value of ‘b’ into the equation.
v. Subtract
from both sides.
vi. Simplify.
vii. Multiply all terms by -2.
viii. Simplify.
A = 1, B = -2 and C = -5
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Standard Form of a Line
~
Student Practice Worksheet
Name____________________________________________Date______________Grade___________
Write an equation in Standard Form given a line in slope-intercept form.
1. y =
2. y =
3. y =
4. y =
5. y =
6. y =
7. y =
8. y =
9. y =
10. y =
Write an equation in Standard Form given two points.
11. (-3, 1) and (5, 4)
12. (5, -6) and (2, 3)
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
13. (2, -2) and (-6, 1)
14. (3, 4) and (-7, 4)
15. (0, -2) and (7, 0)
16. (-5, -1) and (4, -7)
\
17. (1, 0) and (4, 1)
18. (-2, 0) and (0, -2)
19. (-1, -2) and (1, 4)
20. (-2, 5) and (-1, 2)
Write an equation in Standard Form given a point and a Slope.
21. (2, 3), m = 3
22. (-4, 7), m = 3
23. (0, 3), m = -4
24. (7, 2), m = -5
25. (3, 2), m =
26. (2, -3), m =
27. (1, 2), m = 7
28. (3, -1), m = -1
29. (-2, 5), m = -4
30. (3, 5), m =
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Standard Form of a Line
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Student Practice Worksheet
Answer Key
Name______________________________________________ Date______________ Grade_________
Write an equation in Standard Form given a line in slope-intercept form.
1. y =
2. y =
7x – 10y = -8
3. y =
4x + 5y = -5
4. y =
4x + 10y = 3
5. y =
7x + 7y = 4
6. y =
x – 5y = - 5
3x + 7y = -4
7. y =
8. y =
6x + 6y = 1
9. y =
2x + 10y = -7
10. y =
2x – 5y = 2
4x – 7y = -5
Write an equation in Standard Form given two points.
11. (-3, 1) and (5, 4)
3x – 8y = -17
12. (5, -6) and (2, 3)
3x + y = 9
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
(Standard Form Worksheet answer key)
13. (2, -2) and (-6, 1)
3x + 8y = -10
15. (0, -2) and (7, 0)
14. (3, 4) and (-7, 4)
y=4
16. (-5, -1) and (4, -7)
2x – 7y = 14
2x + 3y = - 7
17. (1, 0) and (4, 1)
18. (-2, 0) and (0, -2)
x – 3y = 1
19. (-1, -2) and (1, 4)
3x – y = - 1
x + y = -2
20. (-2, 5) and (-1, 2)
3x + y = -1
Write an equation in Standard Form given a point and a Slope.
21. (2, 3), m = 3
3x – y = 3
23. (0, 3), m = -4
4x + y = 3
25. (3, 2), m =
2x – 3y = 0
27. (1, 2), m = 7
7x – y = 5
29. (-2, 5), m = -4
4x + y = -3
22. (-4, 7), m = 3
3x – y = -19
24. (7, 2), m = -5
5x + y = 37
26. (2, -3), m =
3x + 2y = 0
28. (3, -1), m = -1
x+y=2
30. (3, 5), m =
5x – 3y = 0
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Standard Form of a Line
~
Student Practice Worksheet
Rubric
4
Mechanics
No math errors
Quiz Grading Rubric:
Problem
Total points of
Correct
Answer
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Criteria
3
2
No major math
May be some
errors or serious
serious math
flaws in reasoning. error or flaws in
reasoning.
Problem
1
0
Major math errors Blank
or serious flaws
answers
in reasoning.
Total points of
Correct
Answer
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Total: _______________
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Standard Form of a Line
~
Quiz
Name____________________________________________Date_______________Grade___________
Write an equation in Standard Form given a line in slope-intercept form.
1.
y = -2x – 18
2.
3.
10 – 2x = 8y
4.
5.
y=
y=
Write an equation in Standard Form given a point and a slope.
6.
(2, -4), slope = -1
7.
(3, 1), slope = ½
8.
(-1, 2), slope = 2
9.
(-4, 0), slope = ¾
10.
(-3, -3), slope =
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Write an equation in Standard Form given two points.
11.
(4, -2) and (8, 3)
12.
(2, 10) and (8, 7)
13.
(7, 3) and (8, 5)
14.
(5, 7) and (8, 5)
15.
(10, 3) and (7, 9)
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Standard Form of a Line
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Quiz
Answer Key
Name____________________________________________Date_______________Grade___________
Write an equation in Standard Form given a line in slope-intercept form.
1.
y = -2x – 18
2.
2x + y = -18
3.
10 – 2x = 8y
2x + 15y = 50
4.
x – 7y = 7
x + 4y = 5
5.
y=
y=
5x + y = -4
Write an equation in Standard Form given a point and a slope.
6.
(2, -4), slope = -1
7.
x – 2y = 1
x + y = -2
8.
(-1, 2), slope = 2
2x – y = 4
10.
(3, 1), slope = ½
9.
(-4, 0), slope = ¾
3x – 4y = -12
(-3, -3), slope =
7x – 3y = - 12
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
(Standard Form Quiz Answer Key continue)
Write an equation in Standard Form given two points.
11.
(4, -2) and (8, 3)
12.
5x – 4y = 28
13.
(7, 3) and (8, 5)
2x – y = 11
15.
(2, 10) and (8, 7)
x + 2y = 22
14.
(5, 7) and (8, 5)
2x + 3y = 31
(10, 3) and (7, 9)
2x + y = 23
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Lines, Lines, Lines!!! Standard Form of a Linear Equation
Standard Form of a Line
~
Quiz
Rubric
4
Mechanics
No math errors
Quiz Grading Rubric:
Problem
Total points of
Correct
Answer
1.
2.
3.
4.
5.
6
7
8
Criteria
3
2
No major math
May be some
errors or serious
serious math
flaws in reasoning. error or flaws in
reasoning.
Problem
1
0
Major math errors Blank
or serious flaws
answers
in reasoning.
Total points of
Correct
Answer
9.
10.
11.
12.
13.
14.
15.
Total:_________
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